A Guide to Advanced Real Analysis PDF Download

Author: G. B. Folland
Publisher: American Mathematical Soc.
ISBN: 0883859157
Category : Education
Languages : en
Pages : 107

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Book Description
A concise guide to the core material in a graduate level real analysis course.

Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 0817644423
Category : Mathematics
Languages : en
Pages : 466

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Book Description
* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

Author: Gerald B. Folland
Publisher: John Wiley & Sons
ISBN: 1118626397
Category : Mathematics
Languages : en
Pages : 309

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Book Description
An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.

Author: N. L. Carothers
Publisher: Cambridge University Press
ISBN: 9780521497565
Category : Mathematics
Languages : en
Pages : 420

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Book Description
A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.

Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 0817644415
Category : Mathematics
Languages : en
Pages : 656

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Book Description
Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.

Author: Robert S. Borden
Publisher: Courier Corporation
ISBN: 0486150380
Category : Mathematics
Languages : en
Pages : 421

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Book Description
This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more. Carefully chosen problems appear at the end of each chapter, and this new edition features an additional appendix of tips and solutions for selected problems.

Author: Kenneth A. Ross
Publisher: CUP Archive
ISBN:
Category : Mathematics
Languages : en
Pages : 192

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Book Description

Author: Patrick Fitzpatrick
Publisher: American Mathematical Soc.
ISBN: 0821847910
Category : Mathematics
Languages : en
Pages : 610

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Book Description
"Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."--pub. desc.

Author: Eric Schechter
Publisher: Academic Press
ISBN: 0080532993
Category : Mathematics
Languages : en
Pages : 907

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Book Description
Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/

Author: Halsey Royden
Publisher: Pearson Modern Classics for Advanced Mathematics Series
ISBN: 9780134689494
Category : Functional analysis
Languages : en
Pages : 0

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Book Description
This text is designed for graduate-level courses in real analysis. Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.